Question
Download Solution PDFΔABC ~ ΔPQR, the areas of ΔABC and ΔPQR are 64 cm2 and 81 cm2, respectively and AD and PT are the medians of ΔABC and ΔPQR, respectively. If PT = 10.8 cm, then AD = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
ΔABC ~ ΔPQR
Area of ΔABC = 64 cm2
Area of ΔPQR = 81 cm2
PT = 10.8 cm
AD is the median of ΔABC.
PT is the median of ΔPQR
Concept:
The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides & medians.
\(\text{Area of (ΔABC)}\over{\text{Area of (ΔPQR)}}\) = \(({AD\over PT})^2\)
Calculation:
\(\text{Area of (ΔABC)}\over{\text{Area of (ΔPQR)}}\) = \(({AD\over PT})^2\)
⇒ \(64\over81\) = \(({AD\over PT})^2\)
⇒ \(AD\over PT\) = \(\sqrt{64\over81}\) = \(8\over9\)
⇒ \(AD\over 10.8\) = \(8\over9\)
⇒ AD = \({8\times10.8}\over9\) = 9.6 cm
∴ AD = 9.6 cm
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